{
  "id": 6405,
  "curve_key": "55896935221890272184886056836929:-419595653239016551598179164720664423198542251233",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1164519483789380670518459517436",
    "485643117174787578417565198941268687348908560"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 219.31124140380726,
  "faltings_height": 16.10279611939948,
  "conductor": "924067205461080002728932377057018486310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "31",
    "59",
    "107",
    "263",
    "421",
    "631",
    "56649331198003333129"
  ],
  "discriminant": "-817339230195339457068213486106403890793398374395209101272489394235993751707168205596262400",
  "regulator": "37840654675966.7259066073886520120271416834948251092992251553",
  "points": [
    [
      "437898261936075873464/737881",
      "-1196189679717190724188721138740/633839779"
    ],
    [
      "-15945207290586045511673032/18919727401",
      "76691792196382969544649275932065361684/2602389584280149"
    ],
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      "2267397934451472043837181048/12271282235521",
      "715158470690338560576960118421184631020604/42986780251037248319"
    ],
    [
      "9156962781441400606094456/13219710529",
      "5121645123523086754221847640087109700/1519962657492833"
    ],
    [
      "-35470402535108296/121",
      "37689257503107843188654476/1331"
    ],
    [
      "332555716928519588",
      "-191776038825583231937222284"
    ],
    [
      "137417719585589160487551741092/85476737001769",
      "-41581807330521802334066328284913483835970948/790263461636886047147"
    ],
    [
      "3077482318685240847008306/3236813449",
      "-2840497288648462662439101474367658170/184152027553957"
    ],
    [
      "130540938229859864/961",
      "-541149955153256688322720420/29791"
    ],
    [
      "4168569051331008179600617459832/135628920036289",
      "8505821809998324005788508324750593127450556092/1579532097050981077087"
    ],
    [
      "199850886778370216024837432/117007489",
      "2825263980473103216366267969777447308548/1265670008513"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), t = 2209/947 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-11-02 01:57:09",
  "updated_at": "2026-11-02 01:57:09"
}